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2008

The Factorization Method for Electrical Impedance Tomography in the Half-Space

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The Factorization Method for Electrical Impedance Tomography in the Half-Space
We consider the inverse problem of electrical impedance tomography in a conducting half space, given electrostatic measurements on its boundary, i.e., a hyperplane. We first provide a rigorous weak analysis of the corresponding forward problem, and then develop a numerical algorithm to solve an associated inverse problem. This inverse problem consists in the reconstruction of certain inclusions within the half space, which have a different conductivity than the background. To solve the inverse problem we employ the so-called factorization method of Kirsch, which so far has only been considered for the impedance tomography problem in bounded domains. Our analysis of the forward problem makes use of a Liouville type argument which says that a harmonic function in the entire two dimensional plane must be a constant if some weighted L2 norm of this function is bounded. Key words. Electrical impedance tomography, half space problem, factorization method. AMS subject classifications. 65N21, ...
Martin Hanke, Birgit Schappel
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2008
Where SIAMAM
Authors Martin Hanke, Birgit Schappel
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